Explanation:
The nominal spread (yield spread) is the difference between the YTM of the bond and the YTM (or spot rate) of a risk-free benchmark bond with the same maturity. Since this is a 2-year bond, its yield spread should be calculated relative to the 2-year risk-free rate, not the 6-month spot rate. Therefore, option B is false. Option A is true because the 4.0% continuous rate discounts the cash flows to the market price, meaning it acts as the yield-to-maturity. Option C is true because a decrease in price due to higher credit risk means the required yield and z-spread increase, shifting both the flat YTM curve and the steep z-spread curve upwards. Option D is true because the zero-volatility spread (Z-spread) is the constant spread added to the entire spot curve to match the bond's market price. The difference between the blue line (spot + z-spread) and the lower spot curve is exactly the z-spread (e.g., 4.03% - 1.61% = 2.42%).
Ultimate access to all questions.
No comments yet.
The bond's market price of $103.73 can be computed by discounting its cash flows continuously at 4.0% per annum, which is represented by the flat yellow line. Specifically: $3.00 \cdot \exp(-4% \cdot 0.5) + `3.00` \cdot \exp(-4\% \cdot 1.0) + \`3.00 \cdot \exp(-4\% \cdot 1.5) + \103.00` \cdot \exp(-4\% \cdot 2.0) = \`103.73$. The bond's same market price of $103.73` can also be derived by discounting the same cash flows according to the continuous discount rates given by the steep blue line. The lower steep line, which shows a rate of 0.40% at six months, is actually two nearby curves: a swap rate curve and nearby spot rate curve. Both start at 0.40%, but as the spot rate curve is slightly steeper, by year 2.0, the spot rate is 1.61%, while the swap rate is 1.60%. For this purpose, we assume both the spot and swap are risk-free curves, e.g., US Treasury.
Each of the following is true about this bond EXCEPT which is false?
A
The bond's yield-to-maturity is 4.0%
B
The yield spread, represented by the solid red vertical arrow, is the difference between 4.0% (yellow line) and 0.40% (spot rate at six months)
C
If the price of the bond decreased due solely to perceived credit risk of bond (without any change in market risk), the upper curves (yellow and blue) would shift up
D
The z-spread, represented by the dashed red vertical arrow, is the difference between the (upper steep) blue line and the (lower steep) spot rate; e.g., 2.42% = 4.03% - 1.61%